The Research archive provides access to all Research articles published in past issues of Communications of the ACM.
"Almost-Linear-Time Algorithms for Maximum Flow and Minimum-Cost Flow," by Li Chen et al., comes within striking distance of answering the question: "Does maximum flow have a scalable algorithm?"
We present an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in m1+o(1) time.
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